# Right triangle - 8th grade (13y) - examples

1. The sides 2
The sides of a trapezoid are in the ratio 2:5:8:5. The trapezoid’s area is 245. Find the height and the perimeter of the trapezoid.
2. Horizontal distance
The road has a gradient of 8%. How many meters will the road rise on a horizontal distance of 400m?
3. Pile of sand
A large pile of sand has been dumped into a conical pile in a warehouse. The slant height of the pile is 20 feet. The diameter of the base of the sand pile is 31 feet. Find the volume of the pile of sand.
4. Cincinnati
A map is placed on a coordinate grid. Cincinnati located at (5,4) and San Diego is located at (-10, -3). How far apart is Cincinnati from San Diego on the map? Round to the nearest tenth.
5. Diagonals at right angle
In the trapezoid ABCD this is given: AB=12cm CD=4cm And diagonals crossed under a right angle. What is the area of this trapezoid ABCD?
6. An angle
An angle x is opposite side AB which is 10, and side AC is 15 which is hypotenuse side in triangle ABC. Calculate angle x.
7. Garden
Area of square garden is 6/4 of triangle garden with sides 56 m, 35 m and 35 m. How many meters of fencing need to fence a square garden?
8. Right Δ
Right triangle has length of one leg 28 cm and length of the hypotenuse 53 cm. Calculate the height of the triangle.
9. Axial section
Axial section of the cone is equilateral triangle with area 208 dm2. Calculate volume of the cone.
10. Circle chord
What is the length d of the chord circle of diameter 36 m, if distance from the center circle is 16 m?
11. Rectangle
The rectangle is 11 cm long and 45 cm wide. Determine the radius of the circle circumscribing rectangle.
12. River
Calculate how many promiles river Dunaj average falls, if on section long 957 km flowing water from 1454 m AMSL to 101 m AMSL.
13. Tetrahedral pyramid
What is the surface of a regular tetrahedral (four-sided) pyramid if the base edge a=7 and height v=6?
14. Triangle SAS
Calculate area and perimeter of the triangle, if the two sides are 51 cm and 110 cm long and angle them clamped is 130°.
15. Movement
From the crossing of two perpendicular roads started two cyclists (each at different road). One runs at average speed 28 km/h, the second at average speed 24 km/h. Determine the distance between them after 45 minutes cycling.
16. Square
Points A[-10,-1] and B[2,-1] are adjacent vertices of the square ABCD. Calculate area of the square ABCD.
17. Is right?
Is triangle with sides 51, 56 and 77 right triangle?
18. Cubes
One cube is inscribed sphere and the other one described. Calculate difference of volumes of cubes, if the difference of surfaces in 257 mm2.
19. Cone A2V
Surface of cone in the plane is a circular arc with central angle of 126° and area 415 cm2. Calculate the volume of a cone.
20. Short cut
Imagine that you are going to the friend. That path has a length 330 meters. Then turn left and go another 2000 meters and you are at a friend's. The question is how much the journey will be shorter if you go direct across the field?

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